Thermodynamics of ideal gas in doubly special relativity

We study thermodynamics of an ideal gas in doubly special relativity. A new type of special functions (which we call ``incomplete modified Bessel functions'') emerge. We obtain a series solution for the partition function and derive thermodynamic quantities. We observe that doubly special relativity thermodynamics is nonperturbative in the special relativity and massless limits. A stiffer equation of state is found.

Synthesis, reactivity and structural characterisation of bicyclic tetraphosphapentazanes

The diphenoxy bicyclic tetraphosphapentazane derivatives (EtN)(5)P-4(OPh)(2) 2 and its monoxide (EtN)(5)P-4(O)(OPh)(2) 3 have been prepared. Both 2 and 3 exist as a mixture of two isomers. One isomer of (EtN)(5)P-4(O)(OPh)(2) 3a has been isolated and its reaction with tetrachloro-1,2-benzoquinone yielded (EtN)(5)P-4(O)(OPh)(2)(O2C6Cl4) 5 in which the junction phosphorus atom becomes five-co-ordinated. Treatment of 2 or 3a with [Mo(CO)(4)(nbd)] (nbd = norbornadiene, bicyclo[2.2.1]hepta-2,5-diene), on the other hand, yielded the chelate complex [Mo(CO)(4){(EtN)(5)P-4(O)(n)(OPh)(2)}] (n = 0 or 1; 6 or 7) in which the peripheral phosphorus atoms are bonded to the metal. The structures of 3a and 5-7 have been confirmed by single-crystal X-ray diffraction studies. The two P3N3 rings in 3a and 5 adopt twist/twist and irregular/twist conformations respectively; the phenoxy substituents occupy the 'pseudo axial' positions. However, an ideal chair conformation is observed for the P3N3 rings in 6 and 7 with the phenoxy substituents taking up the 'pseudo equatorial' positions. The NMR spectroscopic data for the compounds are discussed.

Paraxial-wave optics and relativistic front description .1. The scalar theory

With the extension of the work of the preceding paper, the relativistic front form for Maxwell's equations for electromagnetism is developed and shown to be particularly suited to the description of paraxial waves. The generators of the Poincaré group in a form applicable directly to the electric and magnetic field vectors are derived. It is shown that the effect of a thin lens on a paraxial electromagnetic wave is given by a six-dimensional transformation matrix, constructed out of certain special generators of the Poincaré group. The method of construction guarantees that the free propagation of such waves as well as their transmission through ideal optical systems can be described in terms of the metaplectic group, exactly as found for scalar waves by Bacry and Cadilhac. An alternative formulation in terms of a vector potential is also constructed. It is chosen in a gauge suggested by the front form and by the requirement that the lens transformation matrix act locally in space. Pencils of light with accompanying polarization are defined for statistical states in terms of the two-point correlation function of the vector potential. Their propagation and transmission through lenses are briefly considered in the paraxial limit. This paper extends Fourier optics and completes it by formulating it for the Maxwell field. We stress that the derivations depend explicitly on the "henochromatic" idealization as well as the identification of the ideal lens with a quadratic phase shift and are heuristic to this extent.

Interrogating an insect society

Insect societies such as those of ants, bees, and wasps consist of 1 or a small number of fertile queens and a large number of sterile or nearly sterile workers. While the queens engage in laying eggs, workers perform all other tasks such as nest building, acquisition and processing of food, and brood care. How do such societies function in a coordinated and efficient manner? What are the rules that individuals follow? How are these rules made and enforced? These questions are of obvious interest to us as fellow social animals but how do we interrogate an insect society and seek answers to these questions? In this article I will describe my research that was designed to see answers from an insect society to a series of questions of obvious interest to us. I have chosen the Indian paper wasp Ropalidia marginata for this purpose, a species that is abundantly distributed in peninsular India and serves as an excellent model system. An important feature of this species is that queens and workers are morphologically identical and physiologically nearly so. How then does an individual become a queen? How does the queen suppress worker reproduction? How does the queen regulate the nonreproductive activities of the workers? What is the function of aggression shown by different individuals? How and when is the queen's heir decided? I will show how such questions can indeed be investigated and will emphasize the need for a whole range of different techniques of observation and experimentation.

Thermodynamic Properties and Phase Diagram for the System MoO2–TiO2

The activity of molybdenum dioxide (MoO2) in the MoO2–TiO2 solid solutions was measured at 1600 K using a solid-state cell incorporating yttria-doped thoria as the electrolyte. For two compositions, the emf was also measured as a function of temperature. The cell was designed such that the emf is directly related to the activity of MoO2 in the solid solution. The results show monotonic variation of activity with composition, suggesting a complete range of solid solutions between the end members and the occurrence of MoO2 with a tetragonal structure at 1600 K. A large positive deviation from Raoult's law was found. Excess Gibbs energy of mixing is an asymmetric function of composition and can be represented by the subregular solution model of Hardy as follows.The temperature dependence of the emf for two compositions is reasonably consistent with ideal entropy of mixing. A miscibility gap is indicated at a lower temperature with the critical point characterized by Tc (K)=1560 and . Recent studies indicate that MoO2 undergoes a transition from a monoclinic to tetragonal structure at 1533 K with a transition entropy of 9.91 J·(mol·K)−1. The solid solubility of TiO2 with rutile structure in MoO2 with a monoclinic structure is negligible. These features give rise to a eutectoid reaction at 1412 K. The topology of the computed phase diagram differs significantly from that suggested by Pejryd.

Electronic structure and bonding of beta-rhombohedral boron using cluster fragment approach

Theoretical studies using density functional theory are carried out to understand the electronic structure and bonding and electronic properties of elemental beta-rhombohedral boron. The calculated band structure of ideal beta-rhombohedral boron (B-105) shows valence electron deficiency and depicts metallic behavior. This is in contrast to the experimental result that it is a semiconductor. To understand this ambiguity we discuss the electronic structure and bonding of this allotrope with cluster fragment approach using our recently proposed mno rule. This helps us to comprehend in greater detail the structure of B-105 and materials which are closely related to beta-rhombohedral boron. The molecular structures B12H12-2, B28H21+1, BeB27H21, LiB27H21-1, CB27H21+2, B57H36+3, Be3B54H36, and Li2CB54H36, and corresponding solids Li8Be3B102 and Li10CB102 are arrived at using these ideas and studied using first principles density functional theory calculations.

Stereochemical Analysis of Higher α,α-Dialkylglycine Containing Peptides. Characterization of Local Helical Conformations at Dipropylglycine Residues and Observation of a Novel Hydrated Multiple β-Turn Structure in Crystals of a Glycine Rich Peptide

The peptide Boc-Gly-Dpg-Gly-Gly-Dpg-Gly-NHMe (1) has been synthesized to examine the conformational preferences of Dpg residues in the context of a poor helix promoting sequence. Single crystals of 1 were obtained in the space group P21/c with a = 13.716(2) Å, b = 12.960(2) Å, c = 22.266(4) Å, and β = 98.05(1)°; R = 6.3% for 3660 data with |Fo| > 4σ. The molecular conformation in crystals revealed that the Gly(1)-Dpg(2) segment adopts φ, ψ values distorted from those expected for an ideal type II‘ β-turn (φGly(1) = +72.0°, ψGly(1) = −166.0°; φDpg(2) = −54.0°, ψDpg(2) = −46.0°) with an inserted water molecule between Boc-CO and Gly(3)NH. The Gly(3)-Gly(4) segment adopts φ, ψ values which lie broadly in the right handed helical region (φGly(3) = −78.0°, ψGly(3) = −9.0°; φGly(4) = −80.0°, ψGly(4) = −18.0°). There is a chiral reversal at Dpg(5) which takes up φ, ψ values in the left handed helical region. The Dpg(5)-Gly(6) segment closely resembles an ideal type I‘ β-turn (φDpg(5) = +56.0°, ψDpg(5) = +32.0°; φGly(6) = +85.0°, ψGly(6) = −3.0°). Molecules of both chiral senses are found in the centrosymmetric crystal. The C-terminus forms a hydrated Schellman motif, with water insertion into the potential 6 → 1 hydrogen bond between Gly(1)CO and Gly(6)NH. NMR studies in CDCl3 suggest substantial retention of the multiple turn conformation observed in crystals. In solution the observed NOEs support local helical conformation at the two Dpg residues.

Vapor-liquid equilibrium data for the systems diisopropyl ether-n-heptane and diisopropyl ether-carbon tetrachloride at medium pressures

Vapor-liquid equilibrium data for the systems diisopropyl ether-n-heptane and diisopropyl ether-carbon tetrachloride have been reported at pressures of 760, 1520, and 2280 mm. of Hg. The systems form ideal mixtures under the pressure range studied.

Two-Phase Thermodynamic Model for Efficient and Accurate Absolute Entropy of Water from Molecular Dynamics Simulations

Presented here is the two-phase thermodynamic (2PT) model for the calculation of energy and entropy of molecular fluids from the trajectory of molecular dynamics (MD) simulations. In this method, the density of state (DoS) functions (including the normal modes of translation, rotation, and intramolecular vibration motions) are determined from the Fourier transform of the corresponding velocity autocorrelation functions. A fluidicity parameter (f), extracted from the thermodynamic state of the system derived from the same MD, is used to partition the translation and rotation modes into a diffusive, gas-like component (with 3Nf degrees of freedom) and a nondiffusive, solid-like component. The thermodynamic properties, including the absolute value of entropy, are then obtained by applying quantum statistics to the solid component and applying hard sphere/rigid rotor thermodynamics to the gas component. The 2PT method produces exact thermodynamic properties of the system in two limiting states: the nondiffusive solid state (where the fluidicity is zero) and the ideal gas state (where the fluidicity becomes unity). We examine the 2PT entropy for various water models (F3C, SPC, SPC/E, TIP3P, and TIP4P-Ew) at ambient conditions and find good agreement with literature results obtained based on other simulation techniques. We also validate the entropy of water in the liquid and vapor phases along the vapor-liquid equilibrium curve from the triple point to the critical point. We show that this method produces converged liquid phase entropy in tens of picoseconds, making it an efficient means for extracting thermodynamic properties from MD simulations.

Multiple imaging with an aberration optimized hololens array

The imaging performance of hololenses formed with four different geometries were studied through an analysis of their third-order aberration coefficients. It is found that the geometry proposed by Brandt (1969) gives the least residual aberration with minimum variation of this aberration with the reconstruction angle. When the ideal position of one of the construction beams is changed in order to generate a hololens array, the residual aberration is found to increase sharply, which in turn affects the image resolution among the multiplied images in the output. A hololens array was generated using Brandt's geometry with the help of a one-dimensional sinusoidal grating. The results of multiple imaging with the hololens array are presented. The image resolution is reasonably high and can be further improved by reducing the f-number of the hololenses.

Ideal Structure of the Silver Code

The Silver code has captured a lot of attention in the recent past,because of its nice structure and fast decodability. In their recent paper, Hollanti et al. show that the Silver code forms a subset of the natural order of a particular cyclic division algebra (CDA). In this paper, the algebraic structure of this subset is characterized. It is shown that the Silver code is not an ideal in the natural order but a right ideal generated by two elements in a particular order of this CDA. The exact minimum determinant of the normalized Silver code is computed using the ideal structure of the code. The construction of Silver code is then extended to CDAs over other number fields.

Correlation of Oxygen Storage Capacity and Structural Distortion in Transition-Metal-, Noble-Metal-, and Rare-Earth-Ion-Substituted CeO2 from First Principles Calculation

Oxygen storage/release (OSC) capacity is an important feature common to all three-way catalysts to combat harmful exhaust emissions. To understand the mechanism of improved OSC for doped CeO2, we undertook the structural investigation by X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), H-2-TPR (temperature-programmed hydrogen reduction) and density functional theoretical (DFT) calculations of transition-metal-, noble-metal-, and rare-earth (RE)-ion-substituted ceria. In this report, we present the relationship between the OSC and structural changes induced by the dopant ion in CeO2. Transition metal and noble metal ion substitution in ceria greatly enhances the reducibility of Ce1-xMxO2-delta (M = Mn, Fe, Co, Ni, Cu, Pd, Pt, Ru), whereas rare-earth-ion-substituted Ce(1-x)A(x)O(2-delta) (A = La, Y) have very little effect in improving the OSC. Our simulated optimized structure shows deviation in cation oxygen bond length from ideal bond length of 2.34 angstrom (for CeO2). For example, our theoretical calculation for Ce28Mn4O62 structure shows that Mn-O bonds are in 4 + 2 coordination with average bond lengths of 2.0 and 3.06 angstrom respectively. Although the four short Mn-O bond lengths spans the bond distance region of Mn2O3, the other two Mn-O bonds are moved to longer distances. The dopant transition and noble metal ions also affects Ce coordination shell and results in the formation of longer Ce-O bonds as well. Thus longer cation oxygen bonds for both dopant and host ions results in enhanced synergistic reduction of the solid solution. With Pd ion substitution in Ce1-xMxO2-delta (M = Mn, Fe, Co, Ni, Cu) further enhancement in OSC is observed in H-2-TPR. This effect is reflected in our model calculations by the presence of still longer bonds compared to the model without Pd ion doping. The synergistic effect is therefore due to enhanced reducibility of both dopant and host ion induced due to structural distortion of fluorite lattice in presence of dopant ion. For RE ions (RE = Y, La), our calculations show very little deviation of bonds lengths from ideal fluorite structure. The absence of longer Y-O/La-O and Ce-O bonds make the structure much less susceptible to reduction.

A bicharacteristic formulation of the ideal MHD equations

On a characteristic surface Omega of a hyperbolic system of first-order equations in multi-dimensions (x, t), there exits a compatibility condition which is in the form of a transport equation along a bicharacteristic on Omega. This result can be interpreted also as a transport equation along rays of the wavefront Omega(t) in x-space associated with Omega. For a system of quasi-linear equations, the ray equations (which has two distinct parts) and the transport equation form a coupled system of underdetermined equations. As an example of this bicharacteristic formulation, we consider two-dimensional unsteady flow of an ideal magnetohydrodynamics gas with a plane aligned magnetic field. For any mode of propagation in this two-dimensional flow, there are three ray equations: two for the spatial coordinates x and y and one for the ray diffraction. In spite of little longer calculations, the final four equations (three ray equations and one transport equation) for the fast magneto-acoustic wave are simple and elegant and cannot be derived in these simple forms by use of a computer program like REDUCE.

Novel gray coded pattern for unwrapping phase in fringe projection based 3D profiling

A method to reliably extract object profiles even with height discontinuities (that leads to 2n pi phase jumps) is proposed. This method uses Fourier transform profilometry to extract wrapped phase, and an additional image formed by illuminating the object of interest by a novel gray coded pattern for phase unwrapping. Simulation results suggest that the proposed approach not only retains the advantages of the original method, but also contributes significantly in the enhancement of its performance. Fundamental advantage of this method stems from the fact that both extraction of wrapped phase and unwrapping the same were done by gray scale images. Hence, unlike the methods that use colors, proposed method doesn't demand a color CCD camera and is ideal for profiling objects with multiple colors.